Lectures_on_Artificial_Intelligence_08.09.16.pdf

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Artificial Intelligence and Expert Systems
MCA/MSc III

Students are sincerely advised to read various books and consult
internet sites for a detailed clarification of topics presented here.
Contents are illustrated in class rooms so they must attend classes
regularly and attentively. They can however contact teacher at any
time in department.
On suggestions/discussions, the present notes will be modified, so
please keep in touch regularly.
Readings
1. Artificial Intelligence: A Modern Approach; Stuart Jonathan Russell, Peter
Norvig, Prentice Hall, 2010
2. Artificial Intelligence; Elaine Rich, Kevin Knight; Tata McGraw – Hill
Publishing Company, 2005
Few internet sites ( With Acknowledgments to known / unknown sites for
figures / useful literature for academic purpose only)
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Unit-1

Unit 1- Introduction
Definition and Approaches
(By different Scientists/researchers)
The goal of work in artificial intelligence is to build machines that
perform tasks normally requiring human intelligence. (Nilsson, Nils J.
(1971), Problem-Solving Methods in Artificial Intelligence (New York:
McGraw-Hill): vii.)
Research scientists in Artificial Intelligence try to get machines to
exhibit behavior that we call intelligent behavior when we observe it
in human beings. (Slagle, James R. (1971), Artificial Intelligence: The
Heuristic Programming Approach (New York: McGraw-Hill): 1.)
Artificial intelligence (AI) is technology and a branch of computer
science that studies and develops intelligent machines and software.
The exciting new effort to make computers think ... machines with
minds, in the full and literal sense'' (Haugeland, 1985)
The automation of activities that we associate with human thinking,
activities such as decision-making, problem solving, learning ...''
(Bellman, 1978)
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Definition and Approaches
The art of creating machines that perform functions that require
intelligence when performed by people'' (Kurzweil, 1990)
The study of how to make computers do things at which, at the
moment, people are better'' (Rich and Knight, 1991)
The study of mental faculties through the use of computational
models'' (Charniak and McDermott, 1985)
The study of the computations that make it possible to perceive,
reason, and act'' (Winston, 1992)
A field of study that seeks to explain and emulate intelligent behavior
in terms of computational processes'' (Schalkoff, 1990)
AI seeks to understand the working of the mind in mechanistic terms
The branch of computer science that is concerned with the
automation of intelligent behavior'' (Luger and Stubblefield, 1993)
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Conclusion about definition of AI
After an extensive survey of definitions given by scientists and
researchers at different times, we can conclude that
AI is the science of making a machine think and act like an intelligent
person.
Term intelligent person is important to ensure that the actions and
thinking that are being imitated and incorporated in machine should
be rational.
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What is AI?
Views of AI fall into four categories:
Thinking humanly
Thinking rationally
Acting humanly
Acting rationally
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Acting humanly: Turing Test
The Turing Test, proposed by Alan Turing (Turing, 1950), was
designed to provide a satisfactory operational definition of
intelligence. Turing defined intelligent behavior as the ability to
achieve human-level performance in all cognitive tasks, sufficient to
fool an interrogator. Roughly speaking, the test he proposed is that
the computer should be interrogated by a human via a teletype, and
passes the test if the interrogator cannot tell if there is a computer or a
human at the other end.
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Details of following Applications
1.Finance
2.Medical
3.Industries
4.Telephone maintenance
5.Telecom
6.Transport
7.Entertainment
8.Pattern Recognition
9.Robotics
10.Data Mining
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Applications of Artificial Intelligence

Challenges before AI
It is easy said but difficult done, in order to achieve the task of imitating human behaviour
or acquiring human intelligence, a machine (a computer in our case) must reflect the
following capabilities which are commonly inherited by an intelligent person:
Natural language processing : Like a human, a machine should understand the spirit
or the meaning of sentences spoken or written freely in natural language by humans.
We don’t mind grammar as well as composition of sentences while reading or talking
informally.
knowledge representation : It is another great challenge how to express knowledge
which can be presented in mathematical or some logical format. Ultimate goal to get a
work done by a computer will be to translate the informal sentences into formal ones
which could be well interpreted by a computer. We use production systems, semantic
nets, frames like structures to express knowledge.
automated reasoning : The capability to use the stored information to answer
questions and to draw new conclusions;
machine learning : Learning is an important property of humans. Whatever we wish
to act, we learn first then exercise for perfection. A machine should also be able to learn
to adapt to new circumstances and to detect and extrapolate patterns.
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Time Machine for AI Developments
1943 McCulloch Pitts: Boolean circuit model of brain
1950 Turing's Computing Machinery and Intelligence
1956 Dartmouth meeting: Artificial Intelligence adopted
1952—69 Look, Ma, no hands!
1950s Early AI programs, including Samuel's checkers
program, Newell Simon's Logic Theorist,
Gelernter's Geometry Engine
1965 Robinson's complete algorithm for logical reasoning
1966—73 AI discovers computational complexity
Neural network research almost disappears
1969—79 Early development of knowledge-based systems
1980-- AI becomes an industry
1986-- Neural networks return to popularity
1987-- AI becomes a science
1995-- The emergence of intelligent agents
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Achievements in AI
Deep Blue defeated the reigning world chess champion
Garry Kasparov in 1997
Proved a mathematical conjecture (Robbins conjecture)
unsolved for decades
No hands across America (driving autonomously 98% of
the time from Pittsburgh to San Diego)
During the 1991 Gulf War, US forces deployed an AI
logistics planning and scheduling program that involved
up to 50,000 vehicles, cargo, and people
NASA's on-board autonomous planning program
controlled the scheduling of operations for a spacecraft
Proverb solves crossword puzzles better than most
humans
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Intelligent Agents
Agent: In our daily life, an agent is commonly a person who can do our job usually on
some obligation. An agent is anything that can be viewed as perceiving its environment
through sensors and acting upon that environment through effectors. A human agent
has eyes, ears, and other organs for sensors, and hands, legs, mouth, and other body
parts for effectors. A robotic agent substitutes cameras and infrared range finders for
the sensors and various motors for the effectors. A software agent has encoded bit
strings as its percepts and actions; it can produce the square root of any number of any
positive number as an example.
A rational Agent is one which does the things rightly (rationally).
Performance Evaluation of an agent: How correctly or efficiently an agent
serves to our expectation. It could be relative depending on individuals expectations.
Intelligent Agents: Agents which can transform percepts into actions rationally.
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Intelligent Agents
A calculator is also an agent but it provides no intelligence, just a hard core calculation
corrected up to maximum possible value. An intelligent agent on the other hand
involves capability to take decision not up to perfection like a hard core agent. E.g.
diagnosing a patient on the basis of symptoms and predict disease.
An agent is composed of following two components
Agent = architecture + program
An architecture on which an agent resides is a hardware infrastructure like camera,
sensors, videos , computer or any machine. A program usually is a software program to
control the architecture to initiate agent. An example of a taxi drive agent is below
Agent
Type
Percepts Actions Goals Environment
Taxi driver Cameras,
speedometer, GPS,
sonar, microphone
Steer,
accelerate,
brake, talk to
passenger
Safe, fast,
legal,
comfortable
trip,
maximize
profits
Roads, other
traffic, pedestrians,
customers
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Intelligent Agents
After reading the table shown for a taxi driver agent, it is apparent that a taxi driver does
not require to be recognized as a a human or a program. The percepts are components
which agent requires as the inputs like cameras, speedometer to control speed etc.
Types of agent programs
Simple Reflex Agent: When the actions of nearest object are clearly visible then what
response has to be taken, e.g.
If the car going ahead applies brake (as appears from brake lights of the front car), then car following it should
also initiate brake. In other words, take a counter action against an action (reaction vs action)
Agents that keep track of the world
- To know around if some other car is over taking our car then what to do
Goal based agents
- The goal should be known to the agent by means of a sequence of actions to follow during operation. E.g. the
destination should be known to a taxi driver accordingly paths can be derived.
Utility based agents
- The goal should be achieved with some performance measure set by user. The cost, the degree of comfort,
safety could be associated with achieving goals.
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Unit-1 Environments
Accessible
Whether the sensors of the agent can access complete environment or partially.
Deterministic
Whether the next state can be determined by the current state specifically.
Episodic
Whether the environment’s states are available in episodes ( serial parts ) or all at one time
Static
Whether the environment is changing while the agent is working or remains unchanged.
Discrete
Whether the percepts and actions are distinct and limited like moves in a chess game, or
continuous like a running ship/train/non-digital clock (especially seconds arm)/ceiling fan.
Please see notes on Intelligent Agents(Ask me to collect)
Details and further reading at various internet CL/DL books, sites
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Problem Solving
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Unit -2

Unit-2 Problem Solving
Production Systems: Systems that generate (produce) rules (states) to
reach a solution
A production system commonly consists of following four basic components:
1. A set of rules of the form Ci Ai where Ci refers to starting state and Ai represents
consequent state. Also Ci the condition part and Ai is the action part.
2. One or more knowledge databases that contain whatever information is relevant
for the given problem.
3. A control strategy that ascertains the order in which the rules must be applied to the
available database
4. A rule applier which is the computational system that implements the control
strategy and applies the rules to reach to goal (if it is possible).
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State Space
State space search is a process used in which successive or states of an instance are
considered, with the goal of finding a goal state with a desired property.
State space search often differs from traditional search (sequential, indexed sequential,
binary search etc) methods because the state space is implicit: the typical state space
graph is much too large to generate and store in memory. Instead, nodes are generated
as they are explored, and typically discarded thereafter.
E.g. in a tic tack toe game, every move by a player forms a state space and the three
similar (O or X) consecutive (row, column or diagonal) symbols forms goal state.
In a chess game also state space forms a set of moves by players.
We discuss water jug problem in the next section.
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State Space Search
The water jug problem: You are given two jugs, a 4-litre one and a 3-litre
one. Neither has any measuring markers on it. There is a pump that
can be used to fill the jugs with water. How can you get exactly 2 litres
of water into 4-litre jug.
Let x and y be the amounts of water in 4-Lt and 3-Lt Jugs respectively
Then (x,y) refers to water available at any time in 4-Lt and 3-Lt jugs.
Also (x,y) (x-d,y+dd) means drop some unknown amount d of water
from 4-Lt jug and add dd onto 3-Lt jug.
All possible production rules can be written as follows
1. (x, y) → (4, y) if x4, fill it to 4; y remains unchanged
if x 4
2. (x, y) → (x, 3) if y3, fill it to 3; x remains unchanged
if y 3
3. (x, y) → (x − d, y) if there is some water in 4 Lt jug, drop
if x 0 some more water from it
4. (x, y) → (x, y − d) if there is some water in 3 Lt jug, drop
if y 0 some more water from it
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State Space Search
5. (x, y) → (0, y) if there is some water in 4-Lt, empty it, y remains unchanged
if x 0
6. (x, y)→ (x, 0) if there is some water in 3-Lt, empty it, x remains unchanged
if y 0
7. (x, y) → (4, y − (4 − x)) if there is some water in 3-Lt, the sum of
if x + y ≥ 4, y 0 water of 4-Lt and 3-Lt jug is =4, then fill
water in 4-Lt jug to its capacity from 3-Lt jug
8. (x, y) → (x − (3 − y), 3) same as 7 with suitable change in x,y
if x + y ≥ 3, x 0
9. (x, y) → (x + y, 0) if sum of water in both jugs =4, then drop
if x + y ≤ 4, y 0 whole water from 3-Lt into 4-Lt
10. (x, y) → (0, x + y) if sum of water in both jugs =3, then drop
if x + y ≤ 3, x 0 whole water from 4-Lt into 3-Lt
11. (0, 2) → (2, 0) Transfer 2-Lt from 3-Lt jug into empty 4-Lt jug
12. (2, y) → (0, y) Empty 2 Lt water onto ground from 4-Lt jug
without disturbing 3 Lt jug
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State Space Search
Solution of Water Jug Problem
Obviously to solve water jug problem, we can perform following
sequence of actions,
(0,0) (0,3) (3,0) (3,3) (4,2) (0,2) (2,0)
By applying rules 2,9,2,7,5 and 9 with initial empty jugs
Remember: There is NO hard and fast rules to follow this sequence. In
any state space search problem, there can be numerous ways to
solve, your approach can be different to solve a problem and
sequence of actions too.
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State Space Search
Other problems
1. Cannibals and missionaries problems: In the missionaries (humans)and cannibals
(human eaters) problem, three missionaries and three cannibals must cross a river
using a boat which can carry at most two people. At any time number of cannibals on
either side should not be greater than number of missionaries otherwise former will
eat latter. Also The boat cannot cross the river by itself with no people on board.
2. Tower of Hanoi Problem: It consists of three pegs, and a number of disks ( usually
60) of different sizes which can slide onto any peg. The puzzle starts with the disks in
a neat stack in ascending order of size on one rod, the smallest at the top, thus
making a conical shape. The objective of the puzzle is to move the entire stack to
another rod, obeying the following rules:
Only one disk must be moved at a time.
Each move consists of taking the upper disk from one of the rods and sliding it onto another
rod, on top of the other disks that may already be present on that rod.
No disk may be placed on top of a smaller disk.
3. Monkey Banana Problem: A monkey is in a room. A bunch of bananas is hanging
from the ceiling and is beyond the monkey's reach. However, in the room there are
also a chair and a stick. The ceiling is just the right height so that a monkey standing
on a chair could knock the bananas down with the stick. The monkey knows how to
move around, carry other things around, reach for the bananas, and wave a stick in
the air. What is the best sequence of actions for the monkey?
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Search Techniques
Un-informed (Blind) Search Techniques do not take into account the location
of the goal. Intuitively, these algorithms ignore where they are going until they find a
goal and report success. Uninformed search methods use only information available in
the problem definition and past explorations, e.g. cost of the path generated so far.
Examples are
– Breadth-first search (BFS)
– Depth-first search (DFS)
– Iterative deepening (IDA)
– Bi-directional search
For the minimum cost path problem:
Uniform cost search
We will discuss BFS and DFS in next section.
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Un
- informed Search Techniques
Breadth-first search (BFS): At each level, we expand all nodes (possible solutions), if there
exists a solution then it will be found.
Space complexity Order is: O(| V |) where as time complexity is O(| V | + | E | ) a graph with
V vertex vector and E Edges, |V| means cardinality of V
It is complete, optimal, best when space is no problem as it takes much space
Algorithm BFS
The algorithm uses a queue data structure to store
intermediate results as it traverses the graph, as follows:
1. Create a queue with the root node and add its direct children
2. Remove a node in order from queue and examine it
If the element sought is found in this node, quit the search and return a result.
Otherwise append any successors (the direct child nodes) that have not yet been
discovered.
3. If the queue is empty, every node on the graph has been examined – quit the search and
return not found.
4. If the queue is not empty, repeat from Step 2.
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Un-informed Search Techniques
Depth-first search (DFS): We can start with a node and explore with all possible solutions
available with this node.
Time and Space complexity: Time Order is: O(| V | + | E | ) , Space Order is: O(| V |)
It is not complete, non-optimal, may stuck in infinite loop
DFS starts at the root node and explores as far as possible along
each branch before backtracking
1. Create a stack with the root node and add its direct children
2. Remove a node in order from stack and examine it
If the element sought is found in this node, quit the search
and return a result.
Otherwise insert any successors (the direct child nodes)
that have not yet been discovered before existing nodes.
3. If the stack is empty, every node on the graph has been
examined – quit the search and return not found.
4. If the stack is not empty, repeat from Step 2.
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BFS for a water jug problem
(0,0)
(4,0) (0,3)
(4,3)
(0,0) (1,3) (4,3) (0,0) (3,0)
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DFS for a water jug problem
(0,0)
(4,0)
(4,3)
(0,3)
(3,0)
(3,3)
(4,2)
(0,2)
(2,0) 28
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Search Techniques
Informed Search Techniques A search strategy which is better than another
at identifying the most promising branches of a search-space is said to be more
informed. It incorporates additional measure of a potential of a specific state to
reach the goal. The potential of a state (node) to reach a goal is measured through a
heuristic function. These are also called intelligent search
Best first search
Greedy Search
A* search
In every informed search (Best First or A* Search), there is a heuristic function and
or a local function g(n). The heuristic function at every state decides the direction
where next search is to be made.
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Algorithm for Greedy Best First Search
Let h(n) be the heuristic function in a graph. In simple case, let it be the
straight line distance SLD from a node to destination.
1. Start from source node S, determine all nodes outward from S and
queue them.
2. Examine a node from queue (as generated in 1) .
If this node is desired destination node, stop and return success.
Evaluate h(n) of this node. The node with optimal h(n) gives the next
successor, term this node as S.
3. Repeat steps 1 and 2.
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Algorithm for A* Search
Let h(n) be the heuristic function in a graph. In simple case, let it be the
straight line distance SLD from a node to destination. Let g(n) be the
function depending on the distance from source to current node. Thus
f(n) = g(n) + h(n)
1. Start from source node S, determine all nodes outward from S and
queue them.
2. Examine a node from queue (as generated in 1) .
* If this node is desired destination node, stop and return success.
* Evaluate f(n) at this node. The node with optimal f(n) gives the next
successor, term this node as S.
3. Repeat steps 1 and 2.
Time = O(log f(n)) where h(n) is the actual distance travelled from n to
goal
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Best First Search An Example
There are cities in a country (Romania). The task is to reach from A(rad) to B(ucharest)
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Method: Greedy Best First Search: Start from Source (Arad). At each possible outward node n from
S, write the heuristic function h(n). Proceed further in the direction in which h(n) is minimum.
Repeat the exercise till goal (destination- Bucharest ) is achieved
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Method: A* Search: Start from Source (Arad). At each possible outward n, node from S, calculate
f(n)=g(n)+h(n), where the heuristic function is h(n) and the total distance travelled so far is g(n).
Proceed further in the direction in which h(n)( is minimum. Repeat the exercise till goal
(destination- Bucharest ) is achieved
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Method: A* Search: Start from Source (Arad). At each possible outward node from S,
write the heuristic function h(n). Add the total distance travelled so far g(n). Proceed
further in the direction in which h(n)( is minimum. Repeat the exercise till goal
(destination- Bucharest ) is achieved
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Heuristics
Where the exhaustive search is impractical, heuristic methods are
used to speed up the process of finding a satisfactory solution via
mental shortcuts to ease the cognitive load of making a decision.
Examples of this method include using a rule of thumb, an educated
guess, an intuitive judgment, stereotyping, or common sense.
In more precise terms, heuristics are strategies using readily
accessible, though loosely applicable, information to control problem
solving in human beings and machines. Error and trial is simplest
form of heuristics. We can fit some variables in an algebraic equation
to solve it.
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Local Search Algorithms
Generate and Test
1. Generate a possible solution.
2. Test to see if this is actually a solution.
3. Quit if a solution has been found.
Otherwise, return to step 1.
Features:
1. Acceptable for simple problems.
2. Inefficient for problems with large space.
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Local Search Algorithms
Just operate on a single current state rather than multiple
paths
Generally move only to neighbors of that state
The paths followed by the search are not retained hence
the method is not systematic
Benefits:
1. uses little memory – a constant amount for current
state and some information
2. can find reasonable solutions in large or infinite
(continuous) state spaces
where systematic algorithms are unsuitable
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Local Search
State space landscape has two axes
location (defined by states)
Elevation or height (defined by objective function or by
the value of heuristic cost function)
In this figure, the cost refers to global minima and the
objective function refers to global maxima(profit e.g.)
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Local Search
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Local Search: Hill Climbing
Hill Climbing is an iterative algorithm that starts with an arbitrary solution to
a problem, then attempts to find a better solution by incrementally changing
a single element of the solution. If the change produces a better solution, an
incremental change is made to the new solution, repeating until no further
improvements can be found. In simple hill climbing, the first closer node is
chosen, whereas in steepest ascent hill climbing all successors are
compared and the closest to the solution is chosen. Both forms fail if there is
no closer node, which may happen if there are local maxima in the search
space which are not solutions. Steepest ascent hill climbing is similar to best-
first search, which tries all possible extensions of the current path instead of
only one.
Stochastic hill climbing does not examine all neighbors before deciding how
to move. Rather, it selects a neighbor at random, and decides (based on the
amount of improvement in that neighbor) whether to move to that neighbor
or to examine another.
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Local Search: Hill Climbing
Pseudo Algorithm
1. Pick initial state s
2. Pick t in neighbors(s) with the largest f(t)
3. IF f(t) = f(s) THEN stop, return s
4. s = t. GOTO 2.
Features:
Not the most sophisticated algorithm in the world.
Very greedy.
Easily stuck.
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Simple Hill Climbing
1. Evaluate the initial state.
2. Loop until a solution is found or there are no new operators left to be applied:
− Select and apply a new operator
− Evaluate the new state:
if goal then quit
otherwise better than current state - - new current state
Drawbacks: it not try all possible new states!
Gradient Descent
Considers all the moves from the current state.
Selects the best one as the next state.
Example of TSP
Unit
Unit-
-2 Problem Solving
2 Problem Solving
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Unit-3

Unit-3 Knowledge Representation (KR) and Reasoning
In this unit, we discuss and illustrate how knowledge can
be represented. As we saw in first unit that KR is a big
issue in AI. Converting knowledge to formal sentences
which could later be coded is the purpose of KR.
We start with essential structure of KR. We will brief
Natural Language Processing and its importance. We may
utter a sentence in many ways and so can be done by our
friends, others in the world, without altering the meaning.
NLP attempts to read the sentences and provide the
meaning reflected in the sentences which must be same in
all. On many occasions, it does not matter whether the
sentence was stated to represent past, future or present.
The meaning matters.
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There can be basically following three representations to
handle linguistic framework. The branch or study that
covers these three issues is known as Meaning–text theory
(MTT) which is a linguistic framework for the
construction of models of natural language. The theory
provides a large and elaborate basis for linguistic
description and, due to its formal character, the theory
offers itself particularly well to various applications of
computers, including machine translation, phraseology
and lexicography. There can be three levels of
representations: Semantic, Syntactic and morphological.
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1. Semantic Representation: It is a web-like semantic
structure (SemS) which combines with other semantic-
level structures (most notably the Semantic-
Communicative Structure). In simple words, A semantic
network or net is a graphic notation for representing
knowledge in patterns of interconnected nodes and arcs.
The structure should represent some logical or valid
meaning otherwise It will be rejected e.g. Red colorless
apples have no color is semantically wrong and must be
rejected. In common jargon if we say, apple eats monkey
is semantically wrong and will be rejected.
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2. Syntactic representations are implemented using
dependency trees, which constitute the Syntactic
Structure (SyntS). SyntS is accompanied by various other
types of structure, most notably the syntactic
communicative structure and the anaphoric structure.
Alternatively linear sequence of words are transformed
into structures that relates words to each other. If a word
sequence violates the language’s rules, it will be rejected.
E.g. in English, sentence: Savita going is school will be
rejected, as it does not conform to English grammar
rules.
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3. Morphological representations: These are
implemented as strings of morphemes arranged in a
fixed linear order reflecting the ordering of elements in
the actual utterance. For morphological analysis,
individual words of a sentence are placed into their
components and punctuations, special symbols are
separated from the words. E.g. Ram’s house will be
separated in Ram, house, and possessive suffix s (belongs
to, of).
Semantic net will be addressed later in details.
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Propositional logic and predicate logic
Propositional logic is a study of propositions. Each proposition has
either a true or a false value but not both. Propositions can be
represented by variables. Usually symbols P and Q represent
propositions. Propositions are simply the sentences used alone or
combined with other sentences. Hence there can be two types of
propositions: simple proposition and compound proposition. A
simple or atomic proposition does not contain any other proposition
as it’s part e.g. Phantom is a dog. The compound proposition
contains more than one proposition e.g. Rajiv is a boy and he likes
ice cream.
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There can be six types of compound propositions as follows. If p and q are two
propositions (sentences) then
1. Negation ¬p indicates the opposite of p.
2. Conjunction (p ∧ q) indicates that p and q both and are enclosed in parenthesis. P
and q are called conjuncts
3. Disjunction (p ∨ q) indicates that p or q either or both and are enclosed in
parenthesis. P and q are called disjuncts.
4. An implication (p ⇒ q) consists of a pair of sentences separated by the ⇒ operator
and enclosed in parentheses. The sentence to the left of the operator is called the
antecedent, and the sentence to the right is called the consequent.
5. A reduction (p ⇐ q) is the reverse of an implication. It consists of a pair of sentences
separated by the ⇐ operator and enclosed in parentheses. In this case, the sentence to
the left of the operator is called the consequent, and the sentence to the right is called
the antecedent.
6. An equivalence (p ⇔ q) is a combination of an implication and a reduction.
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Propositions can not be vague, they have to be true or false but not both
e.g. following sentences are propositions
5+9 =14
11 + 9 = 17
Socrates was a man
It is raining
It is cold
But following sentences are not propositions
Come here
Stand up
X is less than 5
MCA/MSc III 52

Tautology
In a tautology is a formula or proposition which is true in every possible interpretation.
e.g. p V ¬p is a tautology ( 0 OR 1; T V F )
Men are mortal
Truth Tables: A truth table is a table that contains the propositions, well formed formulae
(wffs) , sentences as symbols or variables such that each of them has a true or false
value only. The table can contain the results due to combining these variables
logically.
Take example sentences to explain following
MCA/MSc III 53
P Q p ^ q p V q p ⇒
⇒
⇒
⇒
q
T T T T T
T F F T F
F T F T T
F F F F T

Strengths and weaknesses of propositional
logic
Propositional logic is easy to represent world knowledge which could be required by
an AI system
Propositional logic is simple to deal with and is declarative.
Propositional logic permits conjunctive/disjunctive/partial/negative information.
Real world facts can be written as well-formed formulas (wffs) e.g.
Socrates is a man SOCRATESMAN
Ramesh is a man RAMESHMAN
It is cold COLD
Propositional logic has very limited expressive power e.g.
Search a candle in all locality shops has a clear meaning to search all
shops in the locality for candle. But propositional logic will require separate
statement for each shop
Propositions could be deceptive or extremely difficult to draw a meaningful
conclusion e.g. IRFANMAN and INZMAMMAN produce totally different assertion
Propositional logic assumes world is all full of facts so constitute wffs accordingly
Reasoning with propositional logic is difficult.
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First Order Logic (FOL) or predicate logic
The limitations of propositional logic can be reduced to some extent by using FOL or
predicate logic
A list of basic components / elements / terms used in predicate logic
Constants: Ramesh, Irfan, 2, 2013, March
Functions: brotherof, gt, lt,..
Variables: x,y,z,..
Predicates have values true or false
A predicate can take arguments e.g. man(Ramesh), gt(3,2)
A predicate with one argument shows property of the bracketed argument or object
e.g. teacher(Mukesh)
A predicate with two arguments relates the arguments with each other e.g.
Brother(Mukesh, Suresh)
A predicate without any argument is a proposition or zero order logic
Quantifiers: Universal ∀ means for all; ∀x: gt (y,x) means for all values of x; y will be
greater than x. Existential quantifier ∃ means there exists at least one x, e.g,
∃x: eq(y,x) means there exists at least one x for which y equals to x.
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Representation of sentences into predicate logic
Suppose we want to convert following sentences into Predicate logic
1. Marcus was a man.
2. Marcus was a Pompeian.
3. All Pompeians were Romans.
4. Caesar was a ruler.
5. All Pompeians were either loyal to Caesar or hated him.
6. Every one is loyal to someone.
7. People only try to assassinate rulers they are not loyal to.
8. Marcus tried to assassinate Caesar.
The sentence wise conversions are displayed as
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1. Man(Marcus)
2. Pompeian(Marcus)
3. ∀x: Pompeian(x) → Roman(x)
4. ruler(Caesar)
5. ∀x: Roman(x) → loyalto(x, Caesar) ∨ hate(x, Caesar)
6. ∀x: ∃y: loyalto(x, y)
7. ∀x: ∀y: person(x) ∧ ruler(y) ∧ tryassassinate(x, y) → ¬loyalto(x, y)
8. tryassassinate(Marcus, Caesar)
Now think how will you prove that Marcus was not loyal to Caesar.
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Few more facts about Marcus
1. Marcus was a man.
2. Marcus was a Pompeian.
3. Marcus was born in 40 AD.
4. All men are mortal
5. Volcano erupted in 79 AD.
6. All Pompeians died in 79 AD.
7. No mortal lives longer than 150 years.
8. It is 2013.
9. Alive means not dead.
10. If some one dies then he is dead at all later times.
In class room, several examples are conducted, however conversions are on next page
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1. man(Marcus)
2. Pompeian(Marcus)
3. born (Marcus, 40)
4. ∀x: man(x) → mortal(x)
5. erupted (volcano, 79)
6. ∀x: Pompeian(x) → died(x,79)
7. ∀x: ∀t1: ∀t2: mortal(x) ∧ born(x,t1) ∧ gt(t2-t1,150) → dead(x,t2)
8. Now=2013.
9. ∀x: ∀t :[alive(x,t) → ¬dead(x,t)] ∧ [¬dead(x,t) → alive(x,t)]
10. ∀x: ∀t1: ∀t2:died(x,t1) ∧ gt(t2,t1) → dead(x,t2)
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Instance and isa relationship in predicate
in man(Marcus), class man is represented using unary predicate.
In instance(Marcus, man) predicate is binary such that first argument is
an instance (element) of the second argument which is usually a class.
In isa(Pompeian,Roman) the subclass (Pompeian) and superclass
(Romans) are used .
Isa relationships simplifies representation of wffs and combines
statements to express knowledge in a shorter version.
e.g.
Dog(Phantom)
Instance(Phantom,dog)
Isa( dog, creatures)
Try more such sentences
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Resolution
Resolution is used to produce proofs for facts represented in sentence forms.
Resolution uses following two steps
a) Conversion of axioms to canonical or clause form
b) Using refutation which means to show that the negation of the statement
produces a contradiction with the known statement (which is a fact)
Conversion from Conjuctive Norm Form CNF to clause form
Suppose we want to convert following wff to clause form (all Romans who know Marcus
either hate Caesar or think that anyone who anyone is crazy)
∀x:[Roman(x) ∧ know(x,Marcus)] → [hate(x,Caesar)∨(∀y: ∃z: hate(y,z) → thinkcrazy(x,y))]
1. In the process of clause form conversion, we will take one by one all
rules.
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Resolution Conversion to clause form
∀x:[Roman(x) ∧ know(x,Marcus)] → [hate(x,Caesar)∨(∀y: ∃z: hate(y,z) → thinkcrazy(x,y))]
1.Eliminate → (e.g. A → B can be replaced by ¬A ∨B)
∀x: ¬[Roman(x)∧know(x,Marcus)] ∨ [hate(x,Caesar)∨(∀y:¬(∃z: hate(y,z) ∨ thinkcrazy(x,y))]
Use property of negation : ¬(¬p) = p;
Apply deMorgan’s laws as follows
¬(a ∧ b) = ¬a ∨ ¬b; ¬(a ∨ b) = ¬a ∧ ¬b
And the quantifiers negations as follows
¬ ∀x: p(x) is same as ∃x: ¬ p(x); and ¬∃x: p(x) same as ∀x: ¬ p(x)
∀x: [¬Roman(x)∨¬know(x,Marcus)] ∨ [hate(x,Caesar)∨(∀y: :∀z: ¬ hate(y,z) ∨ thinkcrazy(x,y))]
Allow each quantifier to bind unique variable (as variables are dummy names)
∀x :p(x) ∨ ∀x:q(x) can be converted to ∀x:p(x) ∨ ∀y: q(y)
Bring all quantifiers to the left of wff in relative order.
∀x: ∀y: ∀z: [¬Roman(x)∨¬know(x,Marcus)] ∨ [hate(x,Caesar)∨(¬hate(y,z) ∨
thinkcrazy(x,y))] This form is prenex normal form, a form in which we have prefix of
quantifiers followed by a matrix (rectangular bracket, free of quantifiers ]
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Resolution Conversion to clause form
Skolem Functions
Existential quantifiers ∃ can be eliminated by assuming that rather than thinking one
anonymous value to satisfy ∃(y), we can have one function to replace ∃(y). As an example
∃(y): president(y) means for some value of y, President(y) holds true. We can transform
this to President(S) to represent specifically S as President. Here S is a Skolem function
without argument. Further, example: everyone has a father is formulated as, ∀x: ∃y:
father-of(y,x) can be written in Skolem function as ∀x: father-of(S(x),x)) to relate S(x) as
father of each x.
Everyone loves someone: ∀x: ∃y: lovedby(y,x) in Skolem function as ∀x:lovedby(S(x),x))
Continuing our original sentence,
At this point all variables are universally quantified, drop each such quantifier from wff
[¬Roman(x)∨¬know(x,Marcus)] ∨ [hate(x,Caesar)∨(¬hate(y,z) ∨ thinkcrazy(x,y))]
Apply associate law a∨(b ∨c) = (a∨b) ∨c to get
¬ Roman(x)∨¬know(x,Marcus) ∨ hate(x,Caesar)∨¬hate(y,z) ∨ thinkcrazy(x,y)
Distributive property is given as follows (although not required in our example)
(a ∧ b) ∨c = (a∨c) ∧ (b∨c)
Exercises with simple, short sentences to be tried by students.
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Unification Algorithm
We know that dog(Boxer) and ¬ dog(Boxer) is a contradiction as both can not be true at the same
time. However dog(Boxer) and ¬dog(Jackie) is not a contradiction. To check a contradiction, there
must be some procedure to match literals and possibility to make them identical. This recursive
procedure is called unification algorithm.
We know that
classmates(Ram, Ramesh) and beats(Ram,Ramesh) can not be unified as both have different
initial predicate symbols (classmates and beats which differ).If both predicate symbols match then only
we can use unification procedure.
Simple examples
Unify Q(x) and P(x) FAIL as literals are different and can not be unified
Unify Q(x) and Q(x) Nil as literals are identical so no scope of unification
Unify P(x) and P(x,y) FAIL as both literals have different number of arguments
Simple examples
Unify P(x,x) and P(y,z)
Here both initial predicate symbols are identical, P so we check number of arguments, which is also
same
Now substitute y/x to get P(y,y) and P(y,z) then take z/y which produces P(z,z) thus (z/y)(y/) is the
total substitution applied to unify the two literals
Avoid substitution like (x/y)(x/z) as they cause inconsistency
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Unification Algorithm
Unify(L1,L2) // unifies two literals L1 and L2
1. If L1 or L2 is a variable or constant, then:
a) If L1 and L2 are identical, then return NIL.
b) Else if L1 is a variable, then if L1 occurs in L2 then return FAIL, else
return {(L2/L1)}.
c) Else if L2 is a variable, then if L2 occurs in L1 then return FAIL, else
return {(L1/L2)}.
d) Else return FAIL.
2. If the initial predicate symbols in L1 and L2 are not identical, then return FAIL.
3. If L1 and L2 have a different number of arguments, then return FAIL
4. Set SUBST to NIL.
5. For i  1 to number of arguments in L1:
a) Call Unify with the ith argument of L1 and the ith argument of L2, putting result in S.
b) If S = FAIL then return FAIL.
c) If S is not equal to NIL then:
i. Apply S to the remainder of both L1 and L2.
ii. SUBST := APPEND(S, SUBST).
6. Return SUBST.
As another example hate(x,y) and hate (Marcus,z) can be unified using (Marcus/x,z/y)
or (Marcus/x,y/z)
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Resolution in propositional logic
Suppose a set of axioms(propositions) is given. Convert all propositions of this set to clause form. The
resolution algorithm is given as follows
Algorithm for propositional resolution
1.Convert all propositions to clause form.
2.Negate P and convert the result to clause form. Add it to the set of clauses.
3.Repeat until either a contradiction is found or no progress is possible.
(a) Take any two clauses as parent clauses.
(b) Resolve these two clauses. The resulting clause is called resolvent.
(c ) if the resolvent is empty clause then a contradiction is found. If not, then add resolvent
to the set of clauses. Suppose following propositions are given and we have to prove R.
MCA/MSc III 66
Given axioms
(propositions)
Clause form No.
P P (1)
(P∧ Q) → R ¬P ∨¬Q∨R (2)
(S ∨ T) → Q ¬S ∨ Q (3)
Separate (3) in CF ¬T ∨ Q (4)
T T (5)

Resolution in propositional logic (To prove R, start with ¬ R)
¬P ∨¬Q∨R ¬ R
¬P ∨¬Q P
¬T ∨ Q ¬Q
¬T T
means that a contradiction is reached, we started with ¬ R and combined all true propositions , thus
our initial assumption was wrong and R is true
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Resolution Proofs in Predicate Logic
In order to prove a fact following algorithm of resolution is applied
Resolution Algorithm (To prove P)
Convert all the propositions (axioms) of F to clause form.
Negate P and convert the result to clause form. Add it to the set of clauses
obtained in 1.
Repeat until either a contradiction is found, no progress can be made, or a
predetermined amount of effort has been expended.
a) Select two clauses. Call these the parent clauses.
b) Resolve them together. The resolvent will be the disjunction of all
the literals of both parent clauses with appropriate substitutions
performed and with the following exception: If there is one pair of
literals T1 and ¬ T2 such that one of the parent clauses contains T1
and the other contains ¬ T2 and if T1 and T2 are unifiable, then neither
T1 nor ¬ T2 should appear in the resolvent. If there is more than
one pair of complementary literals, only one pair should be
omitted from the resolvent.
c) If the resolvent is the empty clause, then a contradiction has been
found. If it is not, then add it to the set of clauses available to the
procedure.
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Resolution Proofs in Predicate Logic
A simple example to prove that Marcus hated Caesar
Suppose following axioms in clause form are given
1. man(Marcus)
2. Pompeian(Marcus)
3. ¬ Pompeian(x1) v Roman(x1)
4. Ruler(Caesar)
5. ¬ Roman(x2) v loyalto(x2, Caesar) v hate(x2, Caesar)
6. loyalto(x3, f1(x3))
7. ¬ man(x4) v ¬ ruler(y1) v ¬ tryassassinate(x4, y1) v ¬ loyalto (x4, y1)
8. tryassassinate(Marcus, Caesar)
Variables in 3,5,6,7, (x1,x2,x3,x4 y) have been used to discriminate from each other
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Prove: hate(Marcus, Caesar) ¬hate(Marcus, Caesar)
¬Roman(Marcus) V loyalto(Marcus,Caesar)
Marcus/x2
5
3
2
7
1
4
8
Marcus/x1
¬Pompeian(Marcus) V loyalto(Marcus,Caesar)
loyalto(Marcus,Caesar)
Marcus/x4, Caesar/y1
¬man(Marcus) V ¬ ruler(Caesar) V ¬ tryassassinate(Marcus, Caesar)
¬ ruler(Caesar) V ¬ tryassassinate(Marcus, Caesar)
¬ tryassassinate(Marcus, Caesar)
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Unsuccessful Attempts at Resolution to prove that Marcus is loyal to Caesar
Prove: loyalto(Marcus, Caesar) ¬loyalto(Marcus, Caesar)
¬Roman(Marcus) V hate(Marcus,Caesar)
Marcus/x2
5
3
2
Marcus/x
1
¬Pompeian(Marcus) V hate(Marcus,Caesar)
hate(Marcus,Caesar)
(a)
hate(Marcus,Caesar) 10
persecute(Caesar, Marcus)
hate(Marcus,Caesar)
9
(b)
:
:
MCA/MSc III 71

Unit-3 Knowledge Representation: Semantic Net(works)
There are four common approaches by which knowledge can be achieved
1.Simple relational knowledge: Using relational databases / tables, various queries can be
answered. E.g
It is easy to answer the queries like what is the age of XAR etc. But who is heaviest? (answer)
2. Inheritable knowledge : Here knowledge is derived from the inheritance properties through
attributes (features) and associated values.
3. Inferential Knowledge: Knowledge comes from predicate wffs like
∀x: man(x) → mortal(x)
4. Procedural Knowledge : Using basic facts and small programs, knowledge can be expressed. E.g
if Den is a bird then we can conclude Den can fly but it can turn out to be wrong if Den is an ostrich
or a any bird which doesn’t fly. However in most cases, it is true.
72
RN Name Age height Weight
1 XAR 11 4.5 75
2 BAS 27 6 75.2

Semantic Net: A semantic network is often used as a form of knowledge
representation by connecting concepts together. It is a directed graph consisting of
vertices which represent concepts and edges which represent semantic relations
between the concepts. E.g see the following semantic net to answer the query ‘can
CPD breathe’? ‘What is the uniform color of CPC’?
73
breathe
mammal
person
Team
MSD CSK
instance
can
Uniform
color
Yellow
isa

Semantic Net: Following sentences are converted to semantic nets
(John is 72” tall and taller than Johnny )
74
Johny
John
72
Greater
than
height
H1 H2
height

Semantic Net: Following sentences are converted to semantic nets
(John gave the book to Johnny )
75
Give
Jonny
agent
John Ev123
instance
B111
object
Book
Beneficiary
instance

Unit-3 Knowledge Representation: Partitioned Semantic Net(works)
76
In many cases, the sentences may not be as straight and simple as seen in
previous examples. Especially when the scope of certain literals of the sentence is
quantified by ∀ (for all) and ∃ (at least one). Under these situations, the sentences may
be partly broken into segments such that each segment has a specific scope. Such
networks where, the scope of the variables in a sentence is separately shown, are called
partitioned semantic networks.
In the next four examples, following sentences are expressed as semantic nets
a)The dog bit the mail-carrier
b)Every dog has bitten a mail carrier
c)Every dog has bitten the constable
d)Every dog has bitten every mail carrier
In (a), there is not more than one dog/mail carrier affected. So no need of partitioning,
in (b), every means ∀ ( thus ∀d: ∃ m:dog(d) ∧ m(mail carrier → bit(d,m) )
In (c ), every dog bits the same constable, so sentence has a generic scope for dogs and
not for constable (i.e. ∀d: dog(d) → bit(d, constable) )
In (d), scope of the sentence is for dogs as well as for mail carrier so ∀quantifier is
connected to both, dogs and mail carriers (∀d: ∀ m:dog(d) ∧ m(mail carrier → bit(d,m) )
The sentences can have a form to envelop the scope of it and secondly the variables
which are attached to quantifiers

MCA/MSc III 77
Unit-3 Knowledge Representation: Partitioned Semantic Net(works)

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Unit-4

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Unit-4 Pattern Recognition:
Pattern classification
Pattern classification or simply classification is the back
bone of Pattern Recognition. Most of the issues in
Pattern Recognition use classification’s
techniques.
In general classification is the process of separating
objects on the basis of classes (or similarity, to be
discussed later) or classifying objects into
different groups such that objects belonging to a
group have something similar than in other
groups.
Alternatively, pattern recognition is the assignment of
a label to a given input value.

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Pattern classification: Supervised or Unsupervised
There can be two situations while classifying objects.
1. Classes of the patterns are given
2. Classes of the patterns are NOT given
While classifying the patterns, case (1) is called supervised classification
while case (2) is known as unsupervised classification.
1. Supervised Classification 2 Unsupervised Classification
(class is given) (class is not given)
In both cases, we have a pattern set of 3 patterns, each consisting of 3 features. The
left figure (1) contains a class while right figure (2) doesn’t.
P# F1 F2 F3 Class
1 4.5 2.3 1.9 1
2 1.8 0.9 5.6 2
3 0.55 3.12 9.1 3
P# F1 F2 F3
1 4 2.3 8
2 8 5.6 12
3 6 2.3 3

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Unit
- 4Pattern Recognition:
Pattern classification: Algorithms
The problems related to classification includes following cases
1. Given a set of patterns, called training data. We are asked to train ourselves for this
data so that later on we would be able to tell the class of any pattern. After
training, we may be presented a pattern from the training data and we are asked to
tell the class of this pattern. This pattern is called test pattern. As this test pattern
is from the given training data, we might answer correctly and the class answered
by us would be compared with that of the training data. If the classes of both
patterns (i.e training and testing) match, then we are correct otherwise wrong.
2. In the above case, if the test pattern is suppose not from the training data and still
we tell the class of a test pattern which is never seen before during training. Then
our prediction might be correct or wrong.
3. If no class is given at all during training data patterns, but they are grouped on the
basis of some similarities within groups. Suppose we are asked to place the test
pattern in one of the groups of the training data, then we may do it correctly such
that test pattern is placed in the genuine group.
Cases 1,2 refer to supervised methods of classification while case 3 belongs to
unsupervised classification.
We also noted that training data set is one which is used to get knowledge whereas
test data is used to test our knowledge. Simple example is when you learn in class,
it is training, but when you take exam, no assistance is available with you, then
your performance is evaluated, what we call is test (exam).

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K-Nearest Neighbor Algorithm: The alternative names of this algorithm are
K-NN
Memory-Based Reasoning
Example-Based Reasoning
Instance-Based Learning
Case-Based Reasoning
Lazy Learning
It is a supervised classification algorithm also called classifier
The idea of a k-nn learning is simple. In this algorithm, k is the number of
nearest neighbors. When we want to find the class of an unknown (or unseen)
test pattern, then decide its class by knowing the class of a pattern which is
nearest to unknown test pattern (k=1). Sometimes due to certain
discrepancies, the nearest neighbor may be a different class pattern, then our
approach would lead to a wrong class of test pattern. In this case it is better to
take more nearest neighbors (k1) and know their classes from training data
set. Take the majority of the classes known from nearest neighbors. For a clear
determination of class, take k as odd (3,5,7,..) so that there is no tie while
taking the majority of classes from nearest neighbors.

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K-Nearest Neighbor Algorithm:
The nearest neighbors are determined by finding the Euclidean distance
between training pattern and testing pattern. Suppose we have 100 patterns
in training data set. To find the class of a test pattern, find out the Euclidean
distance of test pattern from all 100 training patterns. Thus we have 100
values. If we take k=1, then take the training pattern with which test pattern
has minimum value (distance). The class of this pattern (which is already
given in the training data) will be class of the test pattern. If k=3, then take 3
minimum values and see the classes of concerned patterns. The class of the
test pattern will be the class which is given by the majority of the 3 classes.
If P_tr and P_tt are training and test patterns respectively with same number
of features f1,f2,f3. P_tr is represented by P_tr (f1,f2,f3) and P_tt by
P_tt(f1t,f2t,f3t) then the Euclidean distance between these pattern is given by
E_d =
Remember that
(1) The class is not considered while taking Euclidean distance (because you
do not know the class of the test pattern)
(2) The class of the nearest neighbor of the test pattern is checked to decide
the class of the test pattern
***** For numeric examples, refer to class room lectures, books, notes,
internet. For any clarity contact the teacher any time in department
( ) ( ) ( )2
3
3
2
2
2
2
1
1
f
f
f
f
f
f t
t
t
−
+
−
+
−

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Unit
Classifiers and classification accuracy
For the data sets where class of each pattern is given before training and later on
testing, we apply supervised classification techniques (such as k-nn) and predict
the class of the unknown testing pattern by finding the class of its k- nearest
neighbors. The algorithm or technique which is applied for predicting the class is
known as classifier. Out of 100 testing patterns for example, if a classifier predicts
the classes of 80 patterns correctly (and 20 incorrectly) then the classifier is said to
have a classification accuracy of 80%. The performance of a classifier is
normally judged by its classification accuracy. No doubt there can be other factors
also like time, cost, space etc to decide the suitability of a classifier, but for now we
focus on classification accuracy only.
Cross Validation: Suppose we want to develop a classifier, say k-nn for example.
Given a data set, to develop a robust classifier to predict the class of a test pattern,
it is important that the classifier should be able to predict the class of a testing
pattern taken from any part of the data set . For that, we must shuffle the patterns
of the data set randomly and ensuring that the classifier is going to be trained for
every class. For this reason, cross validation technique is applied. In this, the data
set is divided into a whole number of sections, say 5. Then usually we take four
sections for training purpose and one section for testing. We shift training and
testing sections frequently so that all patterns are trained for at least once . These
sections are also called sometimes as folds. Thus in this example, we have five
folds, out of which four are used for training and one for testing. We can also say
that we have 80% training data and 20% testing data. When the unknown pattern
is tested, the classifier would have either seen it during training period or at least
classifier would have trained similar kind of a pattern if not exactly the same
unknown pattern. This will improve the accuracy to some extent.

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Unit
Classifiers and classification accuracy
For the data sets where class of each pattern is given before training and later on
testing, we apply supervised classification techniques (such as k-nn) and predict
the class of the unknown testing pattern by finding the class of its k- nearest
neighbors. The algorithm or technique which is applied for predicting the class is
known as classifier. Out of 100 testing patterns for example, if a classifier predicts
the classes of 80 patterns correctly (and 20 incorrectly) then the classifier is said to
have a classification accuracy of 80%. The performance of a classifier is
normally judged by its classification accuracy. No doubt there can be other factors
also like time, cost, space etc to decide the suitability of a classifier, but for now we
focus on classification accuracy only.
Cross Validation: Suppose we want to develop a classifier, say k-nn for example.
Given a data set, to develop a robust classifier to predict the class of a test pattern,
it is important that the classifier should be able to predict the class of a testing
pattern taken from any part of the data set . For that, we must shuffle the patterns
of the data set randomly and ensuring that the classifier is going to be trained for
every class. For this reason, cross validation technique is applied. In this, the data
set is divided into a whole number of sections, say 5. Then usually we take four
sections for training purpose and one section for testing. We shift training and
testing sections frequently so that all patterns are trained for at least once . These
sections are also called sometimes as folds. Thus in this example, we have five
folds, out of which four are used for training and one for testing. We can also say
that we have 80% training data and 20% testing data. When the unknown pattern
is tested, the classifier would have either seen it during training period or at least
classifier would have trained similar kind of a pattern if not exactly the same
unknown pattern. This will improve the accuracy to some extent.

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MCA/MSc III
Unit
Unsupervised Classification and Clustering
We saw, how, the class of an unknown pattern can be determined using the help
of exiting patterns labeled with class. But there are situations when the class of
none of the patterns is given. For examples, different objects are given to a child
(which we have already done at KG or nursery class level), and he is asked to
separate the objects into groups. The child does not know the names of those
objects, neither there is any label attached to any object. The child will see the
resemblance of an object will try to put it with another object which is quite
similar to the former. In this manner, he can form some groups and in each group
all objects are similar. Moreover an object in a group has maximum similarity with
any other object of that group and more dissimilarity with any object of other
groups. These groups are called clusters. Whenever the child is presented a new
object, he will place that new object into an existing group where this new object
has maximum similarity. This type of classification is called unsupervised
classification. It is commonly known as clustering.
As another example, if hundreds of students are enjoying the musical concert in an
auditorium. There can be traditionally two clusters formed, in one cluster, only
boys and in another cluster, the girls only. There can be boys of different classes in
the cluster of boys (may be MCA, MSc, MA, Ph.D, BA etc), similarly there will be
girls of different classes in the same cluster. We see that there can be many classes
belonging to same cluster but it is meaning less or not known (as it will be difficult
to find out the class of each student in dark). Contrarily there can be many clusters
in a single class. E.g., in an MSc class, there can be two clusters, boys and girls. Or
may be three clusters, one cluster having students wearing sandals, second
cluster’s students wearing shoes and the third cluster’s students wearing slippers.

88
MCA/MSc III
Unit
Unsupervised Classification and Clustering
We saw, how, the class of an unknown pattern can be determined using the help
of exiting patterns labeled with class. But there are situations when the class of
none of the patterns is given. For examples, different objects are given to a child
(which we have already done at KG or nursery class level), and he is asked to
separate the objects into groups. The child does not know the names of those
objects, neither there is any label attached to any object. The child will see the
resemblance of an object will try to put it with another object which is quite
similar to the former. In this manner, he can form some groups and in each group
all objects are similar. Moreover an object in a group has maximum similarity with
any other object of that group and more dissimilarity with any object of other
groups. These groups are called clusters. Whenever the child is presented a new
object, he will place that new object into an existing group where this new object
has maximum similarity. This type of classification is called unsupervised
classification. It is commonly known as clustering.
As another example, if hundreds of students are enjoying the musical concert in an
auditorium. There can be traditionally two clusters formed, in one cluster, only
boys and in another cluster, the girls only. There can be boys of different classes in
the cluster of boys (may be MCA, MSc, MA, Ph.D, BA etc), similarly there will be
girls of different classes in the same cluster. We see that there can be many classes
belonging to same cluster but it is meaning less or not known (as it will be difficult
to find out the class of each student in dark). Contrarily there can be many clusters
in a single class. E.g., in an MSc class, there can be two clusters, boys and girls. Or
may be three clusters, one cluster having students wearing sandals, second
cluster’s students wearing shoes and the third cluster’s students wearing slippers.

89
MCA/MSc III
K-means Clustering
Pseudo code (Simple implementation)
1. Decide the number of clusters k
2. Initialize k- number of centroids (or can take any k number of patterns)
3. Find out the Euclidean distance of every pattern from each of these k-
centroids. Thus we have k-distances of a pattern from these k-centroids.
4. A pattern will belong to a cluster with which its distance is minimum. In case
of a tie, a pattern can reside in any one of the tied up clusters.
5. Find out the belongingness of each pattern. Thus all k-clusters will have some
number of patterns.
6. Now modify each of the k-centroids by taking the means of the coordinates
(feature values) of the patterns of a cluster.
7. If the modified centroid is same as previous centroid, stop, otherwise repeat
steps 3-6.
8. Note the patterns belonging to each cluster.

90
MCA/MSc III
Unit-5

91
MCA/MSc III

92
MCA/MSc III

93
MCA/MSc III

94
MCA/MSc III

95
MCA/MSc III

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MCA/MSc III
Final Words
Most part of the syllabi is covered in this presentation. At some
places, highlights are given, whereas details are given in many
places. The examples have been presented in class rooms.
Moreover a session on LISP is also devoted in class rooms. The
students can however contact me for further readings, handouts or
any other difficulty regarding the course material and topics.
As the presentation will be used by students regularly and
discussed frequently, sometimes, if required, the contents might
be replaced as an improvement to existing material. The students
are therefore advised to see the presentation regularly and/or meet
me in the office for any such improvement.
Best of Luck for semester examinations!
Acknowledgements to known/unknown internet
sites/readings/literature used for complex figures
/symbols/explanations to make presentation more useful and
simple for students.

Lectures_on_Artificial_Intelligence_08.09.16.pdf

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